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TwoRises on Permutation ​

Positions i with p(i+1) = p(i) + 2.

On Permutation

Called as CombinatorialStat(x, "TwoRises"). The head's page has its examples.

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Distribution

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FindStat St000534

The number of 2-rises of a permutation.

ObjectValue
[]0
[1]0
[1,2]0
[2,1]0
[1,2,3]0
[1,3,2]1
[2,1,3]1
[2,3,1]0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000534 has the rest.